{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZA53DVPLCXP5VDWBG5PNGFGE7J","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4d4b6bd0092aaf83692a509f8c0227958167d6905325abb98b3538ee304fe3c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-04T22:12:57Z","title_canon_sha256":"b6aa1fc720b263335fa94823523546093b3118ba396992d8d82e2a79caba806b"},"schema_version":"1.0","source":{"id":"1707.01165","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01165","created_at":"2026-05-18T00:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01165v2","created_at":"2026-05-18T00:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01165","created_at":"2026-05-18T00:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZA53DVPLCXP5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZA53DVPLCXP5VDWB","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZA53DVPL","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:3868a3ed81db76a43e08b9ffc6a6b9e390653dc1710099c8d36c7876f01b9f40","target":"graph","created_at":"2026-05-18T00:39:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In [W. Mader, Connectivity keeping paths in $k$-connected graphs, J. Graph Theory 65 (2010) 61-69.], Mader conjectured that for every positive integer $k$ and every finite tree $T$ with order $m$, every $k$-connected, finite graph $G$ with $\\delta(G)\\geq \\lfloor\\frac{3}{2}k\\rfloor+m-1$ contains a subtree $T'$ isomorphic to $T$ such that $G-V(T')$ is $k$-connected. In the same paper, Mader proved that the conjecture is true when $T$ is a path. Diwan and Tholiya [A.A. Diwan, N.P. Tholiya, Non-separating trees in connected graphs, Discrete Math. 309 (2009) 5235-5237.] verified the conjecture when","authors_text":"Hong-Jian Lai, Jixiang Meng, Liqiong Xu, Yingzhi Tian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-04T22:12:57Z","title":"Connectivity keeping stars or double-stars in 2-connected graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01165","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:999921dedc2f0e9d15d729b7bc16fe47050553f1a0efe09155fe5b32f51ce27b","target":"record","created_at":"2026-05-18T00:39:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4d4b6bd0092aaf83692a509f8c0227958167d6905325abb98b3538ee304fe3c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-04T22:12:57Z","title_canon_sha256":"b6aa1fc720b263335fa94823523546093b3118ba396992d8d82e2a79caba806b"},"schema_version":"1.0","source":{"id":"1707.01165","kind":"arxiv","version":2}},"canonical_sha256":"c83bb1d5eb15dfda8ec1375ed314c4fa79a6c6cd41a3312a2f1690c227aa38a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c83bb1d5eb15dfda8ec1375ed314c4fa79a6c6cd41a3312a2f1690c227aa38a1","first_computed_at":"2026-05-18T00:39:31.069444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:31.069444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9i8Tj6JVj/p4rVlxyqXzJLsmbt0t+KJGuY+MUhWbjbzbhp0DYtoy8BUrwIZqHl3cfa2SEZlP/UePdxHgHN1IAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:31.070153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01165","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:999921dedc2f0e9d15d729b7bc16fe47050553f1a0efe09155fe5b32f51ce27b","sha256:3868a3ed81db76a43e08b9ffc6a6b9e390653dc1710099c8d36c7876f01b9f40"],"state_sha256":"43c53aa4103db931101abb0fdeccbb467e995135f767fa0c86f8781b7c5f9626"}